Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.
In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).
Step-by-step explanation:
A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
The minimum cost will be 1091 units.
Define Vertex Formula.
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
Given expression is,
C = 70,000 - 120x + 0.055x²
For this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, plug in the values and find 'x'
minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )
= 120 / 0.11
= 120 / 0.11
= 1090.90 or 1091 units
Therefore, the minimum cost will be 1091 units.
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manufacture of a certain component requires three different machining operations. machining time for each operation has a normal distribution, and the three times are independent of one another. the mean values are 15, 20, and 30 min, respectively, and the standard deviations are 2, 1, and 1.8 min, respectively. what is the probability that it takes at most 1 hour of machining time to produce a randomly selected component? (round your answer to four decimal places.)
The probability that it takes at most 1 hour of machining time to produce a randomly selected component is 0.04074
we are provided with the independent time which are 15, 20, and 30 min and the respective standard deviations which are 2, 1, and 1.8 min.So the total mean X= 15+20+30 =65, as we know that
Variance = ( standard deviation )²
=> Variance = 2² + 1² + 1.8² = 8.24
since standard deviation = √variance
=>Standard deviation = 2.87
so the z score = X -mean /standard deviation
since here X = 1 hour = 60 mintues
z = 60-65/2.87 = -1.74216
So the probability, P( z≤ -1.74216) = 0.04074
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The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028. In the year 2028, the total average credit card debt for a U.S. household will be $
Step-by-step explanation:
The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.
2028 - 1995 = 33 years, so t = 33
D = 401t + 5940
D = 401(33) + 5940
D = 13,233 + 5940
D = 19,173
Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173
help wanted .............................................................
Answer:
I'm pretty sure the answer would be >
Answer: |-8|>-2
Step-by-step explanation:
Because of the lines on both sides of the "-8" you don't pay attention to the "-" sign. That is because this is an absolute value sign. So instead you would read that as 8 ? -2 and which of course 8 is clearly greater
Hope this helps ;)
Graph the image of △IJK after the following sequence of transformations:
Translation 17 units left and 5 units up
Reflection across the line y=1
Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5
What is a transformation in geometry?A transformation is an operation that changes the location, size and shape of geometric figures.
The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)
The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎
The location of the vertices of the image of ΔIJK following the translation transformation are;
[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]
[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]
[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]
The coordinates of a point following a reflection across the line y = 1 are as follows;
The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;
I'(-3, 13), Relative point I'(-3, 12)
J'(-9, 10) has a relative point at (-9, 9)
K'(-3, 7) has a relative point (-3, 6)
The coordinates of the vertices of the reflected image are therefore;
(x, y) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] (x, -(y - 1))
Which gives;
I'(-3, 12) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)
J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)
k'(-3, 6) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)
Please find attached the image of the ΔIJK following the translation and reflection transformation
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Does the series shown below converge or
diverge?
If convergent, find its sum.
Answer: Diverge Reasoning I took the test
In the first round of math contest, each students had to answer 2 questions. Miriam averaged 76 seconds per question. Jake and Rafael averaged 84 seconds per question, and Sam averaged 80 seconds per question. At the end of the first round, what was the total time for all 4 students?
a) 324 seconds
b) 400 seconds
c) 480 seconds
d) 568 seconds
e) 648 seconds
At the end of the first round, the total time is 648 seconds ( option E )
What is average ?An average is the result that you get when you add two or more numbers together and divide the total by the number of numbers you added together.
For example, if there are 10 students in a class with ages 10, 11, 12, 10, 10,12,12,10,11,12 their average age will be( 10+ 11+12+10+10+12+12+10+11+12)/10
for Mariam her average time is 76 which means her total time is 76× 2= 152
for Jake and Rafael their average time is 84 which means their total time is 84×4= 336
for Sam,his average time is 80 which means is total time is 80×2= 160
therefore the total time spent by the 4 students is 152+336+160=648seconds
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there have been 2 earthquakes in the magnitude range 6.0-7.0 in the san francisco area over the past 30 years. what is the mean recurrence interval of earthquakes in this magnitude range?
The mean recurrence interval between earthquakes of this magnitude range over the previous 30 years essentially has been 4.769230 in a basically sort of big way in a subtle way.
Given, the earthquake's magnitude literally basically is between 6.0 and 7.0 in a very definitely big way, or so they for all intents and purposes thought. occurrences = 2 earthquakes
Duration: 30 years
particularly Mean Earthquake Recurrence Interval,
T=(n+1) / m
Where m = 6+7 / 2 = 6.5 , n = 30
T = ( 30+1)/6.5
= 31/6.5
= 4.769230
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50 POINTS!! NEED HELP
Drag each label to the correct location on the image.
Identify which equations have one solution, infinitely many solutions, or no solution.
Answer:
the label are marked by numbers
A store is instructed by corporate headquarters to put a markup of %67 on all items. An item costing $12 is displayed by the store manager at a selling price of $8
. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
The correct selling price of the item has being solved as $20.04 The error that the manager has made is $12.04
How to solve for the markupGiven that there is a markup, the item that is being sold for 12 dollars would be affected by the percentage of the mark up.
This mark up is a 67% markup
This would be solved as
12$ + 67% of 12$
= $12 + 8.04
= $20.04
Hence the correct selling price is $20.04
Next we would have to find the likely error that the manager has made
= $20.04- $8
= $12.04
The likely error of the manager is $12.04
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We know that the diretrix is at x = 5 and that h = 2. This would make p =
When the directrix is at x = 5 and point in the vertex is at h = 2. Then P would be -3
What is P in parabolic equation?In the equation of parabola, P is defined as the distance between the directrix and the vertex
The vertex is defined by the points V ( h, k )
h is for the x coordinate
k is for the y coordinate
when the directrix is given in the x, we solve for P using h
P = h - point given for directrix
P = 2 - 5
P = -3
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Neel buys 8 dog treats for 4.40. what cost per dog treats
The cost per dog treat is 0.55 dollars
How to determine this,
The cost of 8 dog treats is 4.40 dollars
And the number of 1 dog treat is x dollar
x dollar=4.40 dollars×1 dog treat/8 dog treats
x=0.55 dollar per one dog treat
To complete the table,
For 18 dog treats
when 1 dog treat is 0.55 dollar
18 dog treats is x dollar
x=18 dog treats×0.55 dollar/1 dog treat
x=9.9dollars
For 25 dog treats,
when 1 dog treat is 0.55 dollar
for 25 dog treats is x dollar
x=25 dog treats×0.55 dollar/1 dog treat
x=13.75 dollars
For 6.05 dollars,
when 1 dog treat is 0.55 dollar
x dog treat is 6.05 dollars
x=6.05 dollars×1 dog treat/0.55 dollar
x=11 dog treat
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Answer:
Step-by-step explanation: 0.55
which of the following is a quantitative research method that aims to observe the relationship between an independent variable and a dependent variable? a.) a questionnaire b.) secondary data analysis c.) a focus group d.) an experiment
The correct option is a.) a questionnaire, used as observing the relationship between independent variable as well as a dependent variable is the goal of a quantitative research technique known as employed as.
Define the term quantitative research method?Quantitative methods place an emphasis on accurate measurements or the statistical, quantitative, or numerical evaluation of information gathered through surveys, polls, and other types of research, as well as the manipulation of statistical data that has already been obtained using computing methods.
Quantitative research involves gathering numerical information and using it to understand a specific event or generalise it across groups of individuals.
Its primary attributes are:
Typically, organised research tools are used to acquire the data.Given its high reliability, the research study can typically be replicated or redone.The researcher has a specific study question to which unbiased solutions are sought.Before data is collected, the study's various components are all carefully designed.Numbers and statistics make up data, which are frequently displayed in tables, charts, and other non-textual formats.To know more about the quantitative research method, here
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What is -68 as a quotient of integers?
-68 as a quotient of integers is -680/10.
The given integer is -68.
What is a quotient of integers?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
Here, -68/1
Multiply 10 to both the numerator and denominator, we get
= -680/10
= -68
Therefore, -68 as a quotient of integers is -680/10.
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Select the two values of x that are roots of this equation. 2x2 – 11x + 15 = 0
A.x=3
B.x=6
C.x=5
D.x=5/2
The two values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is ,
2x²– 11x + 15 = 0
Solve the equation and find roots
2x² - 6x - 5x + 15 = 0
Take common elements out
2x(x - 3) - 5(x - 3) = 0
we get the brackets same that means we're on right way,
(2x - 5) (x - 3) = 0
split the values into two and find values,
2x - 5 = 0 and x - 3 = 0
2x = 5 x = 3
x = 5 / 2
Hence, the values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
In words, describe the graph of the proportional relationship.
A line from (0, 0) going through (22.25, 25) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (25, 22.25) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
Answer:
(B) A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
Step-by-step explanation:
You want a description of the graph showing the proportional dependency of cost on weight if a couple of (weight, cost) points are (25, 22.25) and (41, 36.49).
GraphThe independent variable is weight, so the x-axis will be labeled Weight (in pounds). The dependent variable is cost, so the y-axis will be labeled Cost (in dollars). The two given points can be plotted on the graph.
The description from the available answer choices is ...
A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
<95141404393>
How many solutions does the
equation have?
3(d + 11) = 6(d + 33)
a. 0
b. 1
c. infinitely many
Answer: 1 solution
Step-by-step explanation:
3(d+11)=6(d+33)
simplifing the above equation
3d+33=6d+198
3d-6d=198-33
-3d=165
d= -165/3
d=-55
Answer:
b. 1
Step-by-step explanation:
3d + 33 = 6d + 198
3d - 6d = 198-33
-3d = 165
thus, d = -165/3
= -55
In one book, there are 15 lines per page. In another book, there are 90 lines in every 6 pages. Determine whether the ratios of lines to pages are proportional in both books.
The ratios of lines to pages are proportional in both books.
How to calculate the value?From the information, in In one book, there are 15 lines per page.
In another book, there are 90 lines in every 6 pages. Therefore, the number of lines per page will be:
= Number of line / Number of page
= 90 / 6
= 15 lines per page
Therefore since they're the same for both books as we got 15 lines, they're proportional.
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Tommaso and Pietro have each been given 3,818 euro to save for college.
Tommaso wants to invest his money in an account such that his investment
will increase to 1.6 times the initial amount in 6 years. Assume the account
pays a nominal annual interest of r % compounded quarterly.
Determine the value of r. Give your answer as a percentage number, not as
a decimal equivalent. Round to two decimal places.
Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.
How to determine the value of r?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Substituting the given parameters into the formula, we have;
1.6(3,818) = 3,818(1 + r/8)^{8 × 6}
1.6 = (1 + r/8)^{48}
Taking the 48th root of both sides of the equation, we have:
[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]
1.00983983823726 = 1 + 0.125r
0.125r = 1.00983983823726 - 1
0.125r = 0.00983983823726
Interest rate, r = 0.00983983823726/0.125
Interest rate, r = 0.0787
Interest rate, r = 7.87%
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On the first day of an experiment, a scientist counts 31 bacteria. On the eighth day of the experiment, the count is 310,000 bacteria.
How many times greater is 310,000 than 31?
A. 310,000
B. 10,000
C. 1,000
D. 31
5. A road has a 6% downgrade (meaning for every 100 feet you could go horizontally, you go down 6
feet). What is the angle the road makes?
The angle the road makes is 3.43°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
A 6% downgrade means that for every 100 units of horizontal run.
The vertical height decreases by 6 units.
The grade has a downward angle of
tan⁻1(6/100) = 3.43°
Hence, the angle the road makes is 3.43°
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In a certain chemical the ratio of zinc to copper is 4 to 11. a jar of the chemical contains 484 grams of copper. how many grams of zinc does it contain
The jar of chemicals contains 176 grams of zinc.
Using ratio and proportion to calculate the amount of zinc. Let us assume the mass of zinc to be x. Equating the ratios.
4 : 11 = x : 484
Rewriting the equation in terms of x
x = (484 × 4) ÷ 11
Performing multiplication in numerator on Right Hand Side of the equation to find the value of x
x = 1936 ÷ 11
Performing division on Right Hand Side of the equation to find the value of x
x = 176
Thus, the mass of zinc is 176 grams.
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I need this answer as soon as possible.It will be nice if you do it in a paper.
Answer:
as shown in underline ^^
Step-by-step explanation:
Fill in the missing words:
When a solid mixes with a liquid and becomes part of the liquid it dissolves.
A solid that dissolves in a liquid is soluble.
A solid that does not dissolve in a liquid is insoluble.
PLEASE HELP will mark brainliest
The slope of the given line in the graph is 0.
What is slope?
The steepness and direction of a line are measured by its slope. Any two points along the line can be used to calculate it. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The Slope, also known as the Gradient, of a straight line displays how steep the line is. The change in y coordinate relative to the change in x coordinate is known as the slope of an object.
Here the given graph points are,
[tex](x_1-y_1)=(1,1)\\(x_2,y_2)=(4,1)[/tex]
Using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{1-1}{4-1}[/tex]
=> slope m = 0/3
=> slope m=0.
Therefore slope of the line is 0.
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A) A box of mass 9 kg contains x articles each of mass 1.2 kg. Write down an expression for the total mass of the box and its contents.
B) How many articles are there in the box if the total mass of the box and articles is 21 kg?
Step-by-step explanation:
A. total mass = 9 + (x × 1.2)
B. 21 - 9 = 12kg
12 ÷ 1.2 = 10 articles.
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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? Round your answer to four decimal places.
The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1
How to determine the probability value?From the question, the given parameters about the distribution are
Mean diameter = 127Variance = 36 The actual data value, x = Less than 0.5The standard deviation is the square root of variance
So, we have
Standard deviation = 6
The z-score is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (0.5 - 127)/6
Evaluate
z = -21.08
The probability is then calculated as:
P(x > 0.5) = P(z > -21.08)
From the z table of probabilities, we have;
P(x < 0.5) = 1
Hence, the probability is 1.0
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Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
I think so ya is does you just need to tell your teacher if you don't understand
a sock drawer contains 10 white socks, 6 black socks , and 8 blue socks if 2 socks are chosen at random, without replacement
calculate the probability she chooses 2 socks of the same colour
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
calculate the probability she chooses 2 socks of the same colour ?I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.
If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%
But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%
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Graph the line with slope 1 passing through the point -2, -5 .
~Shown Graph and Question~
Answer: y = x - 3
Step-by-step explanation:
Answer:
y = x+3
Step-by-step explanation:
First of all we have to find the equation of the line
Slope-intercept form is:
[tex]y=mx+b[/tex]
Putting the value of slope
[tex]y=x+b[/tex]
Putting the point in the equation
(-4,-1)
[tex]-2=-5+b\\b=-2+5\\b=3[/tex]
So the equation is:
[tex]y=x+3[/tex]
The graph is attached with the answer
Keywords: Equation of line, slope
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Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
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